Use ternary search.

Simple math problem. You should just maximise one function.

Unfortunately, I don't know how to maximize it. So I can search :)

H/2*sin(a) - h*tan(a)

Can anybody tell me how to maximize it?

Oh, I recalled my differential calculus.

how you got h*tan(a) in your formula ??? why it works ??

As of the definition of the tangent, there  must be h/tan(a) but this gives wroung results ! why ?